So, what are the similarities and differences between them? Why the similar name? And if anyone can give me an easy definition of script that would be cool..
JavaScript is a name that is licensed to Mozilla by Sun Microsystems. Technically speaking, only Mozilla can use the name "JavaScript". The Microsoft version used to be called JScript. The Adobe version is called ActionScript (ActionScript eventually turned out to be its own sorta language that vaguely conforms to ES standards).
Because ECMAScript is just a specification, it is up to the implementors to conform or not to the spec. Mozilla itself does a lot of weird stuff that doesn't actually conform to the spec. But for the main uses, all three major engines(V8, Spidermonkey and Chakra) are all pretty okay.
If you learn JS for use in node.js, then you are mainly learning the quirks of V8's implementation (of which thankfully are minimal). You may think that V8/Chrome is the dominant JS engine out there, but there are some softwares like CouchDB which uses SpiderMonkey as its engine.
In the past, I believe there used to be a mini language out of Java, also called Java Script, but that quickly fell out of use.
JavaScript as a language was designed to look similar to Java, to catch on the Java-is-the-best-thing-since-sliced-bread bandwagon in the early 1990s. Of course, when you mix paradigms, you have weird shit like ASI in JavaScript.
source: I am writing a couple of books about JavaScript.
This is a topic that is well documented. You can check the wikipedia pages for both Java and javascript.
Alternatively check this http://stackoverflow.com/a/245069
Furthermore, Java is a compiled language, whilst JavaScript is an interpreted language (with lots of JIT tricks in some implementations, e.g. V8).
Once you start digging deeper you'll notice that other than the superficial similarity due to the curly bracket, C-derived syntax, they are extremely different languages. Even the "class based" and "prototype based" core paradigms are very different. Of course, with Java being first, a lot of folks are trying to force JavaScript to be like Java, e.g. writing code with classes - which is a kludge at the best of time.